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A341072 Number of compositions of 2n into n Fibonacci parts.

%I A341072 #13 May 02 2022 03:03:36
%S A341072 1,1,3,7,23,71,231,750,2479,8251,27673,93248,315515,1071097,3646618,
%T A341072 12445982,42571327,145895599,500855361,1722062265,5929045173,
%U A341072 20439121983,70539320558,243695962031,842704577995,2916613479471,10102511916071,35018749192885
%N A341072 Number of compositions of 2n into n Fibonacci parts.
%H A341072 Alois P. Heinz, <a href="/A341072/b341072.txt">Table of n, a(n) for n = 0..1000</a>
%F A341072 a(n) = A121548(2n,n).
%F A341072 a(n) ~ c * d^n / sqrt(n), where d = 3.532272846853808150678856189005437981671101510837727... and c = 0.2903295565097076269212760734928134309226027... - _Vaclav Kotesovec_, Feb 14 2021
%p A341072 g:= proc(n) g(n):= (t-> issqr(t+4) or issqr(t-4))(5*n^2) end:
%p A341072 b:= proc(n, t) option remember;
%p A341072       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341072       `if`(g(j), b(n-j, t-1), 0), j=1..n)))
%p A341072     end:
%p A341072 a:= n-> b(2*n, n):
%p A341072 seq(a(n), n=0..35);
%t A341072 g[n_] := g[n] = With[{t = 5*n^2}, IntegerQ@Sqrt[t+4] || IntegerQ@Sqrt[t-4]];
%t A341072 b[n_, t_] := b[n, t] =
%t A341072      If[n == 0, If[t == 0, 1, 0], If[t < 1, 0, Sum[
%t A341072      If[g[j], b[n - j, t - 1], 0], {j, 1, n}]]];
%t A341072 a[n_] := b[2n, n];
%t A341072 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, May 02 2022, after _Alois P. Heinz_ *)
%Y A341072 Cf. A000045, A121548, A341071.
%K A341072 nonn
%O A341072 0,3
%A A341072 _Alois P. Heinz_, Feb 04 2021